Question

What times what equals 24 and sums to 11

Answer 1

Ok since _x_=24+11 well lets rephrase the equation _x_+11=24 so lets find _ and _ we can find it easily by subtract 24-11=13 but if you multiply 13x1= 13 add 13+1 = 24 your answer would be 13,1

Answer 2

xy = 24
x + y = 11

x + y = 11
- x - x
y = -x + 11


xy = 24
x(-x + 11) = 24
x(-x) + x(11) = 24
-x² + 11x = 24
- 24 - 24
-x² + 11x - 24 = 0
-1(x²) - 1(-11x) - 1(24) = 0
-1(x² - 11x + 24) = 0
-1 -1
x² - 11x + 24 = 0
x² - 8x - 3x + 24 = 0
x(x) - x(8) - 3(x) + 3(8) = 0
x(x - 8) - 3(x - 8) = 0
(x - 3)(x - 8) = 0
x - 3 = 0 or x - 8 = 0
+ 3 + 3 + 8 + 8
x = 3 or x = 8

x + y = 11
3 + y = 11
- 3 - 3
y = 8
(x, y) = (3, 8)

x + y = 11
8 + y = 11
- 8 - 8
y = 3
(x, y) = (8, 3)

The two numbers that add up to 11 and multiply to 24 are 8 and 3.